Theresa May’s Brexit deal will be “dead” if MPs reject if for a fourth time, ministers have admitted.

Brexit Secretary Steve Barclay acknowledged it would be the end of the road for the deal thrashed out with the European Union if the Withdrawal Agreement Bill (WAB) is defeated when it is brought to the Commons in June.

Defeat would also deal a heavy blow to the Prime Minister’s already fragile authority and, although the WAB vote would not be a formal confidence motion, Number 10 sources acknowledged its significance “won’t be underestimated”.

The legislation writes the Brexit agreement into law and represents a fresh attempt to secure Parliament’s support for a deal which has already been rejected three times by MPs, including the heaviest defeat ever suffered by a Government.

Mr Barclay said the WAB would be published as soon as possible and would have its second reading in the Commons, the first legislative hurdle it would have to clear, in the week beginning June 3.

He told the Lords EU Committee: “I think if the House of Commons does not approve the WAB then the (Michel) Barnier deal is dead in that form.”

Number 10 said efforts were continuing to find a “sustainable” majority for the deal, with discussions involving DUP and Labour MPs.

Brexit Secretary Steve Barclay said the deal would be ‘dead’ if the legislation is defeated (Stefan Rousseau/PA)

Asked whether the vote would be considered a “confidence” vote for the Prime Minister, a source said: “That’s not the world that we are currently in but clearly the significance of this piece of legislation can’t and I suspect won’t be underestimated.”

The Prime Minister has already said she will step down once the first phase of the Brexit process is completed and will meet senior Tories on the executive of the backbench 1922 Committee to discuss her future on Thursday.

Mrs May insisted the legislation delivers on Brexit.

Speaking after attending an international summit in Paris, the Prime Minister said: “What we have been doing is talking with the official opposition, we have been talking with MPs across the House looking at the issues that they have had concerns with in relation to the deal that we agreed with the European Union.

“What this Bill does is delivers on Brexit.

“When MPs come to look at this Bill, when they come to vote on this legislation, I’m sure that they will be thinking of the duty that we have to ensure that we deliver on the vote of the British people.

“This is the Bill that delivers Brexit.”

Both Mr Barclay and International Trade Secretary Liam Fox warned Eurosceptics that the possibility of Brexit not happening at all would increase if the WAB was defeated.

(PA Graphics)

That would leave just two options when the October 31 deadline looms, a no-deal Brexit, which has previously been rejected by MPs, or the revocation of Article 50, cancelling the entire process.

Cross-party Brexit talks between Labour and the Tories have so far failed to produce a compromise agreement.

Jeremy Corbyn’s spokesman repeatedly said the party would not support the WAB if no cross-party agreement was reached, but refused to say whether Labour MPs would abstain, which could allow the Bill to receive its second reading, or vote against it and potentially consign it to defeat.

The spokesman said that unless there was an agreement based on “real compromise and movement by the Government” then the WAB would be “based on the same botched Brexit deal that has been rejected three times already by Parliament”.

The spokesman said the talks with the Government were “not an unlimited process” and Labour had “serious concerns about negotiating with a government that is in the process of disintegration” because any deal struck with Mrs May could be scrapped by her replacement.

At Prime Minister’s Questions, Mrs May was challenged by Tory Eurosceptic Peter Bone, who said activists in his constituency favoured a no-deal Brexit and wanted her to quit before the May 23 European elections.

Theresa May speaking during Prime Minister’s Questions in the House of Commons earlier (UK Parliament/Jessica Taylor/PA)

He told the Press Association “I just don’t follow the logic” of bringing the deal back to the Commons.

It was “the definition of madness to keep repeating the same thing and expecting to have a different result”.

Former Brexit minister Steve Baker also questioned the Prime Minister’s decision to bring the legislation for her “failed deal” before Parliament and suggested it would do little to counter the threat posed by Nigel Farage’s Brexit Party.

He said: “If the Brexit Party were demanding we pass this Withdrawal Agreement, a vote might just make sense.

“But they aren’t. Quite the reverse.

“And driving it through over the heads of the DUP appears to eradicate the Government’s majority.”

DUP Westminster leader Nigel Dodds said: “Unless she can demonstrate something new that addresses the problem of the backstop then it is highly likely her deal will go down to defeat once again.”

Tory and Labour officials were continuing the efforts to reach an agreement on Wednesday and the Prime Minister’s Brexit negotiator Olly Robbins was in Brussels for a second day of talks about the potential to make changes to the Political Declaration setting out the future UK-EU relationship.

The legislation will go before the Commons in the same week US President Donald Trump, who has repeatedly spoken out about the Brexit process, is due to make a state visit to the UK.

Mr Trump and his wife Melania will be in the UK from June 3 to June 5.

On June 6, a by-election will also be held in Peterborough to find a replacement for MP Fiona Onasanya, who lost her seat through a recall petition after serving time in prison for lying about a speeding offence.

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